1 /*
2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2010 INRIA Saclay
4 * Copyright 2011 Sven Verdoolaege
5 *
6 * Use of this software is governed by the MIT license
7 *
8 * Written by Sven Verdoolaege, K.U.Leuven, Departement
9 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
10 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
11 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
12 */
13
14 #define xSF(TYPE,SUFFIX) TYPE ## SUFFIX
15 #define SF(TYPE,SUFFIX) xSF(TYPE,SUFFIX)
16
17 /* Given a basic map with at least two parallel constraints (as found
18 * by the function parallel_constraints), first look for more constraints
19 * parallel to the two constraint and replace the found list of parallel
20 * constraints by a single constraint with as "input" part the minimum
21 * of the input parts of the list of constraints. Then, recursively call
22 * basic_map_partial_lexopt (possibly finding more parallel constraints)
23 * and plug in the definition of the minimum in the result.
24 *
25 * As in parallel_constraints, only inequality constraints that only
26 * involve input variables that do not occur in any other inequality
27 * constraints are considered.
28 *
29 * More specifically, given a set of constraints
30 *
31 * a x + b_i(p) >= 0
32 *
33 * Replace this set by a single constraint
34 *
35 * a x + u >= 0
36 *
37 * with u a new parameter with constraints
38 *
39 * u <= b_i(p)
40 *
41 * Any solution to the new system is also a solution for the original system
42 * since
43 *
44 * a x >= -u >= -b_i(p)
45 *
46 * Moreover, m = min_i(b_i(p)) satisfies the constraints on u and can
47 * therefore be plugged into the solution.
48 */
SF(basic_map_partial_lexopt_symm,SUFFIX)49 static TYPE *SF(basic_map_partial_lexopt_symm,SUFFIX)(
50 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
51 __isl_give isl_set **empty, int max, int first, int second)
52 {
53 int i, n, k;
54 int *list = NULL;
55 isl_size bmap_in, bmap_param, bmap_all;
56 unsigned n_in, n_out, n_div;
57 isl_ctx *ctx;
58 isl_vec *var = NULL;
59 isl_mat *cst = NULL;
60 isl_space *map_space, *set_space;
61
62 map_space = isl_basic_map_get_space(bmap);
63 set_space = empty ? isl_basic_set_get_space(dom) : NULL;
64
65 bmap_in = isl_basic_map_dim(bmap, isl_dim_in);
66 bmap_param = isl_basic_map_dim(bmap, isl_dim_param);
67 bmap_all = isl_basic_map_dim(bmap, isl_dim_all);
68 if (bmap_in < 0 || bmap_param < 0 || bmap_all < 0)
69 goto error;
70 n_in = bmap_param + bmap_in;
71 n_out = bmap_all - n_in;
72
73 ctx = isl_basic_map_get_ctx(bmap);
74 list = isl_alloc_array(ctx, int, bmap->n_ineq);
75 var = isl_vec_alloc(ctx, n_out);
76 if ((bmap->n_ineq && !list) || (n_out && !var))
77 goto error;
78
79 list[0] = first;
80 list[1] = second;
81 isl_seq_cpy(var->el, bmap->ineq[first] + 1 + n_in, n_out);
82 for (i = second + 1, n = 2; i < bmap->n_ineq; ++i) {
83 if (isl_seq_eq(var->el, bmap->ineq[i] + 1 + n_in, n_out) &&
84 all_single_occurrence(bmap, i, n_in))
85 list[n++] = i;
86 }
87
88 cst = isl_mat_alloc(ctx, n, 1 + n_in);
89 if (!cst)
90 goto error;
91
92 for (i = 0; i < n; ++i)
93 isl_seq_cpy(cst->row[i], bmap->ineq[list[i]], 1 + n_in);
94
95 bmap = isl_basic_map_cow(bmap);
96 if (!bmap)
97 goto error;
98 for (i = n - 1; i >= 0; --i)
99 if (isl_basic_map_drop_inequality(bmap, list[i]) < 0)
100 goto error;
101
102 bmap = isl_basic_map_add_dims(bmap, isl_dim_in, 1);
103 bmap = isl_basic_map_extend_constraints(bmap, 0, 1);
104 k = isl_basic_map_alloc_inequality(bmap);
105 if (k < 0)
106 goto error;
107 isl_seq_clr(bmap->ineq[k], 1 + n_in);
108 isl_int_set_si(bmap->ineq[k][1 + n_in], 1);
109 isl_seq_cpy(bmap->ineq[k] + 1 + n_in + 1, var->el, n_out);
110 bmap = isl_basic_map_finalize(bmap);
111
112 n_div = isl_basic_set_dim(dom, isl_dim_div);
113 dom = isl_basic_set_add_dims(dom, isl_dim_set, 1);
114 dom = isl_basic_set_extend_constraints(dom, 0, n);
115 for (i = 0; i < n; ++i) {
116 k = isl_basic_set_alloc_inequality(dom);
117 if (k < 0)
118 goto error;
119 isl_seq_cpy(dom->ineq[k], cst->row[i], 1 + n_in);
120 isl_int_set_si(dom->ineq[k][1 + n_in], -1);
121 isl_seq_clr(dom->ineq[k] + 1 + n_in + 1, n_div);
122 }
123
124 isl_vec_free(var);
125 free(list);
126
127 return SF(basic_map_partial_lexopt_symm_core,SUFFIX)(bmap, dom, empty,
128 max, cst, map_space, set_space);
129 error:
130 isl_space_free(map_space);
131 isl_space_free(set_space);
132 isl_mat_free(cst);
133 isl_vec_free(var);
134 free(list);
135 isl_basic_set_free(dom);
136 isl_basic_map_free(bmap);
137 return NULL;
138 }
139
140 /* Recursive part of isl_tab_basic_map_partial_lexopt*, after detecting
141 * equalities and removing redundant constraints.
142 *
143 * We first check if there are any parallel constraints (left).
144 * If not, we are in the base case.
145 * If there are parallel constraints, we replace them by a single
146 * constraint in basic_map_partial_lexopt_symm_pma and then call
147 * this function recursively to look for more parallel constraints.
148 */
SF(basic_map_partial_lexopt,SUFFIX)149 static __isl_give TYPE *SF(basic_map_partial_lexopt,SUFFIX)(
150 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
151 __isl_give isl_set **empty, int max)
152 {
153 isl_bool par = isl_bool_false;
154 int first, second;
155
156 if (!bmap)
157 goto error;
158
159 if (bmap->ctx->opt->pip_symmetry)
160 par = parallel_constraints(bmap, &first, &second);
161 if (par < 0)
162 goto error;
163 if (!par)
164 return SF(basic_map_partial_lexopt_base,SUFFIX)(bmap, dom,
165 empty, max);
166
167 return SF(basic_map_partial_lexopt_symm,SUFFIX)(bmap, dom, empty, max,
168 first, second);
169 error:
170 isl_basic_set_free(dom);
171 isl_basic_map_free(bmap);
172 return NULL;
173 }
174
175 /* Compute the lexicographic minimum (or maximum if "flags" includes
176 * ISL_OPT_MAX) of "bmap" over the domain "dom" and return the result as
177 * either a map or a piecewise multi-affine expression depending on TYPE.
178 * If "empty" is not NULL, then *empty is assigned a set that
179 * contains those parts of the domain where there is no solution.
180 * If "flags" includes ISL_OPT_FULL, then "dom" is NULL and the optimum
181 * should be computed over the domain of "bmap". "empty" is also NULL
182 * in this case.
183 * If "bmap" is marked as rational (ISL_BASIC_MAP_RATIONAL),
184 * then we compute the rational optimum. Otherwise, we compute
185 * the integral optimum.
186 *
187 * We perform some preprocessing. As the PILP solver does not
188 * handle implicit equalities very well, we first make sure all
189 * the equalities are explicitly available.
190 *
191 * We also add context constraints to the basic map and remove
192 * redundant constraints. This is only needed because of the
193 * way we handle simple symmetries. In particular, we currently look
194 * for symmetries on the constraints, before we set up the main tableau.
195 * It is then no good to look for symmetries on possibly redundant constraints.
196 * If the domain was extracted from the basic map, then there is
197 * no need to add back those constraints again.
198 */
SF(isl_tab_basic_map_partial_lexopt,SUFFIX)199 __isl_give TYPE *SF(isl_tab_basic_map_partial_lexopt,SUFFIX)(
200 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
201 __isl_give isl_set **empty, unsigned flags)
202 {
203 int max, full;
204 isl_bool compatible;
205
206 if (empty)
207 *empty = NULL;
208
209 full = ISL_FL_ISSET(flags, ISL_OPT_FULL);
210 if (full)
211 dom = extract_domain(bmap, flags);
212 compatible = isl_basic_map_compatible_domain(bmap, dom);
213 if (compatible < 0)
214 goto error;
215 if (!compatible)
216 isl_die(isl_basic_map_get_ctx(bmap), isl_error_invalid,
217 "domain does not match input", goto error);
218
219 max = ISL_FL_ISSET(flags, ISL_OPT_MAX);
220 if (isl_basic_set_dim(dom, isl_dim_all) == 0)
221 return SF(basic_map_partial_lexopt,SUFFIX)(bmap, dom, empty,
222 max);
223
224 if (!full)
225 bmap = isl_basic_map_intersect_domain(bmap,
226 isl_basic_set_copy(dom));
227 bmap = isl_basic_map_detect_equalities(bmap);
228 bmap = isl_basic_map_remove_redundancies(bmap);
229
230 return SF(basic_map_partial_lexopt,SUFFIX)(bmap, dom, empty, max);
231 error:
232 isl_basic_set_free(dom);
233 isl_basic_map_free(bmap);
234 return NULL;
235 }
236